The eigenvector associated with the smallest eigenvalue is proportional to the quasi-stationary distribution (QSD). It corresponds to the eigenmode exhibiting the slowest decay and limiting the no-passage distribution in the asymptotic time limit [1]}, [2]}. The QSD is observed to considerably contribute to the first-passage and no-passage distributions in applications [3]}. It completely characterizes them when trapping is severe and has an energetic origin. However, for purely entropic traps, it is observed that many additional eigenmodes are necessary to capture the early stage absorption kinetics [3]} correctly. Consequently, the computational cost increases with the number of significant eigenmodes. In this work, we investigate the ability of model order reduction techniques based on Krylov subspace projection and eigenvalue deflation to faithfully characterize the early-stage kinetics at a reduced cost, given an initial probability vector.
